Special Relativity: 4 - Past, Future and Causality

0:06 In the last video we talked about uh how different observers in different frames of reference will perceive different sets of events as simultaneous. So the basic uh picture that we got in in a short description is if we have observers A and B and this is the uh the time axis of A and the spatial axis of A. Then if we look at observer B and observer B is moving relative to A. Then it could be that their time axis looks like this and their spatial axis the sets of events that they consider to be simultaneous

0:52 that's supposed to be uh B will be tilted up like this. So while a will see you know some set of events occurring then another set of events occurring then another set of of events occurring uh and see each of these lines as being simultaneous with time increasing in that direction then observer B will say no I see this set of events all happening at the same time and then this set of events all happening at the same time and this set of events and increasing with time increasing for them in this direction. So if different observers in different frames of reference are disagreeing on

1:39 things as simple as what events are happening simultaneously. What does this do to our understanding of what is the future and what is the past? And also does this have an effect on our notion of causality? the idea that a cause must come before an effect in order for you know the universe to work in a in a logical way. So let's take to try and answer this question. Let's take a look at a at another space-time diagram. Okay. So we have our spatial axis and our time axis. And and just for this one, I'm going to draw an extra spatial axis uh going in and out of the in and out of the monitor. So here here's uh

2:28 here's two spatial axes. And let's say that I'm sitting at a certain moment in time at a certain position right in the center of this uh of this diagram. Well, if I were to turn on a light and just emit beams of light in every direction, then the beam of light going forward would would move like this. The beam of light going backwards would move like this. And and they'd go go out of the out of the screen and into the screen. And on this diagram, as time goes on, they would form this uh cone shaped object. And this is what we consider our future

3:14 light cone, our future light cone. And the reason that we call it that is because inside this cone are all of the events, all of the uh positions and times of uh of different locations in the spacetime that I can get to traveling at the speed of light or less than the speed of light. So, if I want to uh if I want to get to a certain location here, then I can I can, you know, fly a little ship right over there and and make it there. If I want to get to some point out here, well, even if I'm traveling at the speed of light, I'm I'm not going to be able to I'm not going to be able to make it there in time because we can't

4:00 go faster than the speed of light. So, we can consider this set of events to be our future. And in order to understand uh how what we consider to be the past, we can do exactly the thing but going backwards in time. We can draw another cone, another cone backwards in time and say that if you're in this cone, you can send a message to me that is going again at or below the speed of light. If I have uh let's draw use another color for for what's in our pass. If I'm over here at this position in time and I want to affect something here, I can send a

4:45 signal and it can make it there in time. If I'm over here and I try to send the signal, even if it's going at the speed of light, it's not going to it's not going to make it in time. So this cone here is what we consider to be our past. The set of events in spaceime that can affect us at this moment in time and at this position and at uh this moment in time. And we could look at points that uh aren't right at the origin. Let's say we're looking at a point over here. And we'll say that it has a future. So that's our future light cone and it has a past as well. There's a set of events.

5:32 If you're if you're in this past light cone, you can have an effect. You you can send a signal to this point in space and time. And if you're starting at this point in space and time, you can affect anything in the future that is within this cone. So that gives us a nice picture of how we perceive the future of some point or the past of some point. But what about all of this extra space out here that that just uh isn't a part of our future and our past? Uh how do we come to terms with with what's happening there? Well, let's consider another space-time diagram because because that's how we how we answer a lot of these questions. And let's say on this diagram, I'm gonna

6:19 make this one pretty big. Let's say I have uh three events. Okay, so I have event one, I have event two, and I have event, let's put it over here, event three. So according to observer A. So this is again time of A scaled and this is the spatial direction of A of observer A. A will say well all of these events happen at the same time. Then all of these events happen at the same time. Then all of these events happen at the same time. So observer one will say one happens then two happens

7:06 and then three happens. Well, what will observer B say about that? So, let's uh put the time axis and our spatial axis of B. So, this is XB. So, B says that all of these events happen at the same time. All of these events happen at the same time. a little crooked, but that's okay. And all of these events happen at the same time. So observer B will say that two happened first, then one happened, and then three

7:52 happened. Now, a couple of things are going on here. I'm going to I'm going to redraw these three points. I'm just moving it down on on the picture. So, this was event one. This was event three and this was event two. Now in for both of these observers they will say that one happened before three. Okay. So observer A says that observer B says that. And the reason for that is because if I draw my little future light cone of one, three will be inside of that light cone. Or so three is in the future of one. Or

8:40 uh conversely, if I draw the past light cone of three, if I draw the past light cone of three, point one is in the past of three. So if these two points are within each other's are within each other's future or past light cones then not only will uh will person agree that one happened before three but all observers will say that one happens before three. So these two things can affect each other and I could send a signal from from one to three and say one caused three and and causality is matched. But for point two, there's a disagreement

9:27 between the two observers in which happened first. Observer A will say one happened before two. Observer two will say that two happened before one. But and and that is because two is outside of the future or past like cone of one. So we can't say which happened first. It will depend on your observer. But the nice thing is is that signals can't go faster than the speed of light. So you couldn't have some signal that's that's being uh emitted from one to two at faster than the speed of light. You can't say that uh two is caused by one because you'd have to go faster than the speed of light in order for that to happen. And this is the reason why uh

10:15 people say that if I could go faster than the speed of light, I could go backwards in time. If I made it from 0.1 to 0 2, let's say I was looking at uh looking at the frame of A. If I went from point one to point two, you'd say I'm going faster than the speed of light, but I'm still in the future because A is saying that this occurred before this. But observer B will say that no, in my perspective, you just went back in time by going faster than the speed of light. So hopefully this gives you a little bit of an idea of uh of the idea of an object's future and an object's past and

11:03 how the rest of this space out here, we sometimes call it causally disconnected. From this point, I can't affect anything out here and I can't be affected by anything out there. And all observers will agree on